an:05659495
Zbl 1187.82076
Levin, David A.; Luczak, Malwina J.; Peres, Yuval
Glauber dynamics for the mean-field Ising model: cut-off, critical power law, and metastability
EN
Probab. Theory Relat. Fields 146, No. 1-2, 223-265 (2010).
00255622
2010
j
82C20 60J10 60K35
Ising model; Glauber dynamics; Markov chains; Curie-Weiss model; mixing time; cut-off; coupling; meta-stability; heat-bath dynamics; mean-field model
One considers Glauber dynamics for the Ising model on sequences of transitive graphs. It is shown that the system exhibits a cut-off for values of the absolute temperature \(T\) larger than the unity. When \(T=1\), one can obtain the order \(n^{3/2}\) of the mixing time, and the meta-stability of the system is analyzed when \(T\) is small. In this case, it is shown that the mixing time is logarithmic
Guy Jumarie (Montr??al)